Maximum entropy inference of reaction-diffusion models

TL;DR

This paper introduces a maximum entropy-based formalism for constructing reaction-diffusion models that can incorporate diverse experimental data, extending existing frameworks to nonlinear systems and demonstrating its application to biological and ecological examples.

Contribution

It develops a novel maximum entropy formalism for reaction-diffusion models, extending Schr"odinger bridge and Maximum Caliber frameworks to nonlinear interacting systems.

Findings

Successfully modeled morphogen distribution in zebrafish fin

Captured toad population dynamics matching experimental data

Extended maximum entropy methods to nonlinear reaction-diffusion systems

Abstract

Reaction-diffusion equations are commonly used to model a diverse array of complex systems, including biological, chemical, and physical processes. Typically, these models are phenomenological, requiring the fitting of parameters to experimental data. In the present work, we introduce a novel formalism to construct reaction-diffusion models that is grounded in the principle of maximum entropy. This new formalism aims to incorporate various types of experimental data, including ensemble currents, distributions at different points in time, or moments of such. To this end, we expand the framework of Schr\"odinger bridges and Maximum Caliber problems to nonlinear interacting systems. We illustrate the usefulness of the proposed approach by modeling the evolution of (i) a morphogen across the fin of a zebrafish and (ii) the population of two varieties of toads in Poland, so as to match the experimental data.